УДК 620.179
SIGN LEAST MEAN SQUARES-BASED DECONVOLUTION TECHNIQUE FOR ULTRASONIC IRIS APPLICATIONS
M.S. Mohammed*, Kim Ki-Seong** Department of Mechanical Design Engineering, Chonnam National University,
Yeosu 550-749, Korea * E-mail: msiddeq@gmail.com
** E-mail: sngkim@chonnam.ac.kr
Abstract: Sign LMS algorithms, members of the simplified adaptive least-mean squares class, have been developed to reduce computational complexity and simplify hardware implementation. These advantages make them suitable to utilize in ultrasonic IRIS units, a class of applications requiring simple and efficient signal processing algorithms. This paper proposes a specific sign LMS adaptive filters-based deconvolution technique for IRIS applications. It extracts only two of the interface echoes replications for enhanced resolution and quality-enriched presentation; this technique is named "selective deconvolution". Resolution enhancement and presentation's quality enrichment performance among the different sign LMS algorithms were investigated by experiments, and based on performance, the methods themselves were compared. Computational requirements are also presented. The proposed technique with the various adaptive sign LMS filters gave satisfactory results; sign data LMS was found to be the best technique for IRIS applications.
Key words: IRIS pig. adaptive LMS, sign LMS, resolution, selective deconvolution.
СПОСОБ ОБРАТНОЙ СВЕРТКИ УЛЬТРАЗВУКОВЫХ СИГНАЛОВ НА ОСНОВЕ МЕТОДА НАИМЕНЬШИХ КВАДРАТОВ В ПРИМЕНЕНИИ К УЛЬТРАЗВУКОВОЙ СИСТЕМЕ IRIS
М.С. Мохаммед, Ким Ки-Сеонг Отдел разработки механических устройств, Национальный университет Чоннам, Йосу 550-749, Корея
Адаптивные алгоритмы, основанные на методе наименьших квадратов, были разработаны с целью уменьшить сложность вычислений и упростить их аппаратную реализацию. Эти преимущества делают их пригодными для использования в у. з. системах, в частности IRIS, где требуются простые и эффективные алгоритмы обработки сигналов. Предложены специальные адаптивные фильтры на основе обратной свертки, которые применяют в системе IRIS. Фильтр извлекает только два компонента эхосигнала для получения качественных коротких сигналов и улучшения разрешающей способности. Этот способ обработки назван авторами "selective deconvolution" — селективная обратная свертка. Представлено экспериментальное исследование различных алгоритмов обработки эхосигналов. По итогам экспериментов проведено сопоставление эффективности алгоритмов, указаны требования к объемам и точности вычислений. Предложенные способы обработки у. з. сигналов дали удовлетворительные результаты.
Ключевые слова: снаряд IRIS, адаптивный алгоритм по методу наименьших квадратов, знаковый алгоритм по методу наименьших квадратов, разрешение, селективная де-конволюция.
1. INTRODUCTION
Ultrasonic internal rotary inspection system (IRIS) uses the immersion pulse echo technique, considered to be a state-of-the-art piping and pipeline surveillance technique. For the implementation of this technique, a probe is located in an internal rotating turbine with a 45-degree sound reflector; the reflector mirror rotates sending ultrasonic signals to the pipe's wall.
The wall thickness range of the targeted items is likely to contain thin walls and if any metal loss defects are present even smaller thickness are expected to occur, for this reason, time resolution issues need to be resolved. Moreover, noise due to both harsh operation conditions at petrochemical plants and numerous surrounding instruments further deteriorate the resolution.
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Many deconvolution techniques that have been investigated for resolution enhancement in ultrasonic applications are effective [1] and [2]. Tong feng et al. used the conventional LMS adaptive algorithm due to its effectiveness, low computational complexity, and simplicity in resolving the temporal degradation caused by the narrow bandwidth of the transducer in ultrasonic nondestructive inspection [3]. Real-time deconvolution of ultrasonic signals in scattering media, called multi-pattern adaptive deconvolution, which based on taking several reference signals from different depths, was proposed [4].
The computational cost of digital signal processing algorithms for ultrasonic NDT instruments is often complex. The sign LMS algorithms were initially developed to simplify the computational requirement of the adaptive LMS. In this paper, we suggest the use of sign LMS algorithms, namely, sign LMS, sign-data and sign-sign for ultrasonic IRIS units signal processing due to their simplicity and computational efficiency. They will carry out a specific deconvolution technique for ultrasonic IRIS applications to improve resolution and to obtain quality-enriched presentations by extracting only two replications of the interface echoes. This process is called "selective deconvolution".
2. THEORETICAL BASIS
The adaptive LMS algorithms are reviewed [5]:
2.1. Standard LMS
Figure 1 illustrates an adaptive filter. The following equations describes the LMS algorithm
y(n) = £ f^wi (n) x (n - i), (1)
where y(n) is the filter output, x(n - i) is the filter input and wi(n) represent the filter tap weights. The tap weights w0(n), w1(n)^wN-1(n) are selected so that the difference (error)
e(n) = d(n) - y(n), (2)
is minimized in mean-square-error sense, where e(n) is the error signal and d(n) is the desired output. The filter weights are updated as follows:
w(n + 1) = w(n) + 2|e(n)X(n), (3)
where X(n) is the input signal vector and | is the step-size parameter.
Fig. 1. LMS adaptive deconvolution.
Equation (1) is referred to as filtering, equation (2) is used to calculate the estimation error; and equation (3) is the tap-weight adaptation recursion.
2.2. Sign algorithm
Obtained from the conventional LMS by replacing e(n) with its sign, this leads to the following recursion:
w(n + 1) = w(n) + 2|sign{X(n)}. (4)
2.3. Sign-data algorithm
Obtained from the conventional LMS by replacing the input tap vector X(n) with the vector sign {X(n)}, the sign data algorithm recursion becomes:
w(n + 1) = w(n) + 2|e(n)sign{X(n)}. (5)
2.4. The sign-sign algorithm
This algorithm combines the sign and sign data recursions, to give the following:
w(n + 1) = w(n) + 2|sign{e(n)}sign{X(n)}. (6)
2.5. Selective Deconvolution Approach
In ultrasonic NDT signal deconvolution, the characteristics of the reference signal introduce peaks reduction on the filter output. We define the term "maintenance behavior" as the tendency of the filter to preserve the input signal peak values at the output. Selective deconvolution technique aims to control the maintenance behavior of the filter to process and restore only two echoes of the front and back wall interface replica while eliminating the rest by experimentally setting the filter parameters (filter length and step size) and the reference signal properties (shape, position, amplitude).
The first two echoes in the replica next to the front and back surfaces reflections are chosen for selective processing because the front surface echo has a large amount of energy, which results in a wide pulse, which in turn makes it difficult to distinguish from the back surface echo.
3. EXPERIMENTAL SETUP AND RESULTS
An immersion pulse-echo setup was employed, consisting of a 10 MHz immersion probe equipped with turbine and sound reflector, water tank, 1.6 mm-
Fig. 2. Reference signal.
thick stainless steel plate and oscilloscope. Data acquisition system and the adaptive filters were designed in Laboratory Virtual Instrument Engineering Workbench (LABVIEW) graphical programming environment.
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The reference signal was taken as the back wall echo (fig. 2) of a 8.5 mm-thick stainless steel pipe's wall. The reference signal was chosen with properties
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Fig. 3. a — original waveform; b — sign LMS; c — sig data LMS; d — sign-sign LMS.
that could effect the proposed selective deconvolution, and adaptive filter parameters were selected by trial-and-error. The resolution enhancement performance of the different algorithms is shown in fig. 3.
4. DISCUSSION
The original waveform (fig. 3a) shows the difficulty of resolving the much overlapped first and second interface reflections (demarcated area in fig. 3a). The chosen reference signal and filter parameters successfully resolved the targeted echoes and eliminated the rest in the proposed selective deconvolution procedure.
Fig. 3b—d illustrate the action of the different sign LMS algorithms, all filters resolved closely spaced echoes of the 1.6 mm plate showing slight difference in performance. The sign algorithm retained the highest value of the peaks amplitude. The sign-data LMS produced the best performance among the rest considering its ability to shrink the low amplitude hash between and around the echoes.
The sign-data LMS algorithm was selected to be used for IRIS applications. The signals processed with sign-data algorithm were displayed in IRIS data acquisition system (A- end B-scan), white Gaussian noise with 0.15 standard deviation was added to the acquired waveform to simulate the expected circumstances at inspection sites and to examine the algorithm's performance in such conditions. The results are shown in figure 4; the sign-data LMS clearly resolved
the targeted interface reflections. Furthermore, the A- and B-scan displays quality was significantly improved by the removal of interface reflection replications. Noise did n
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